One debater comforted the world. The other frightened it.

THE PRESIDENTIAL debate Monday did not absorb just Americans; it was closely followed by adversaries and allies of the United States across the globe. Many of the latter will have new cause for alarm as they reflect on a string of ignorant misstatements and irresponsible assertions by Donald Trump.

Start with Japan, the closest U.S. ally in Asia, bound to Washington by a mutual defense treaty. Mr. Trump declared: “We can’t defend Japan” because “they do not pay us.” That will be news in Tokyo, which annually budgets some $4 billion to cover the costs of American bases — so much that some analysts estimate it is cheaper to keep 54,000 military personnel in Japan than it would be to return them to the United States. That’s not to speak of the contribution Japan makes to defending vital U.S. interests, such as checking aggression by China and North Korea. The government of Shinzo Abe recently fought to modify the constitution so as to make deeper defense cooperation with the United States possible. Yet Mr. Trump suggests that his administration would not continue this vital alliance because “we’re losing a fortune.”

The same goes for the NATO alliance, which has kept democratic Europe secure for 65 years. Mr. Trump made some cavalier comments about an “obsolete” transatlantic alliance earlier this year, at a time when, as he conceded Monday, he hadn’t “given lots of thought to NATO.” Remarkably, with six weeks to go until the presidential election, he seems to have done no more thinking, or learning. He said NATO countries “should at least be paying us what they are supposed to be paying by treaty and contract.” But there are no such treaties or contracts; NATO is a mutual defense pact.

Mr. Trump also claimed that after he said that NATO should devote itself to terrorism, it set up a “major terror division.” (He said he learned this from a newspaper article.) Could he really be unaware, as Hillary Clinton pointed out, that the only time NATO’s mutual defense article has been invoked was after Sept. 11, 2001, and that NATO has been fighting terrorism in Afghanistan ever since? Apparently so.

The GOP candidate’s flights of fancy must have prompted some amusement as well as alarm in foreign capitals. Take his assertion that the Iranian nuclear deal should have required Tehran to “do something with respect to North Korea” and its nuclear arsenal because “Iran has power over North Korea.” Or consider Mr. Trump’s claim that “had we taken the oil . . . ISIS would not have been able to form . . . because oil was their primary source of income.” But the Islamic State obtained the majority of its oil from Syria. Is Mr. Trump saying that the United States should have invaded that country to seize its wells?

Unfortunately, Mr. Trump’s ludicrous assertions have serious implications. As Ms. Clinton put it, “words matter when you run for president.” She added, “I want to reassure our allies in Japan and South Korea and elsewhere that we have mutual defense treaties and we will honor them.” No doubt U.S. allies will be comforted if she wins in November. Between now and then, like a lot of Americans, they will fear for their future.